Fun with infinite series

Does 0.999… = 1? And Are Divergent Series the Invention of the Devil?

Which refers to a saying by Niels Henrik Abel

The divergent series are the invention of the devil, and it is a shame to base on them any demonstration whatsoever. By using them, one may draw any conclusion he pleases and that is why these series have produced so many fallacies and so many paradoxes …

This reminded me about a fuss in the blogosphere a few months ago:

Some other comments:

While I majored in physics at Carleton I also took more math than was required, enough to appreciate limits and convergence, and to see the dangers in saying that a non-convergent series is equal to anything. But it is kind of fun.

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